Why does E=MC²?

Let's find out.

[@FatherManus]

Because Albert E is as dope as two rappers.

[@Foivos_Apollon]

Unfortunately that hyperbole, mc² is the same as mcc so he's only as good as 1½ rappers

[@sumejividi6663]

Tf are these comments 💀

[@misterdeedeedee]

oh please, he's like a ti82 (ooo) at best

[@zxqwerxz]

Epic rap battles of history!

[@feynstein1004]

@@misterdeedeedee Ooh

[@mariogranados170]

I used to be confused about this equation, but now that I have watched this video, I am even more confused 😅. Thanks!!

[@user-bx5on9hh5f]

I upticked this comment because it made me laugh out loud literally - I'm not saying anything bad about the video; it actually helped me understand it a lot better, but I don't feel like I completely grok it yet.

[@lucas56sdd]

I'll need to watch this a few more times to fully get it, but understanding that we're all moving in spacetime at c really clicked for me from this video. Thanks!

[@ButWhySci]

Yea it seems this wasn't as easy as to follow for viewers as I thought. I realize I have no idea how this video would come across without prior knowledge of some of the concepts I take for granted (eg; we are moving through spacetime at c). I probably need a focus group. I am hesitant to do this as it would make the creation process even longer. But it's likely where I will need to go if I want to improve.

[@evildeadspace]

​@@ButWhyScinah your work is cool. If I can't fully comprehend something right now, it boosts my curiosity about this and gives motivation to know more Also your videos are funny 😊

[@marsdriver2501]

@@ButWhySci I love how your videos go to such depth, it always gives some new perspective on the subject. Being confused forces to think 😈

[@Shreyy17]

Thanks for admitting! Thanks for these videos!

[@PeteskiPotato]

@@ButWhySci This was pretty good to be honest, but might need a reshuffle to be clearer. Maybe talk to a friend that does UX and ask about the wireframing process and Lean UX methodologies. You'll be surprised how fast you can iterate complex ideas into something simple. I'll volunteer for the focus group though 😁

[@algolin]

There is actually a reason why momentum is conserved. It's called Noether's theorem, which says, that for every symmetry of a system there is a quantity that is conserved. Momentum conservation corresponds to translational invariance.

[@HomeofLawboy]

Yes, but this kinda just shifts the question

[@algolin]

@@HomeofLawboy To "Why there is a symmetry?"? That's a much more fundamental question. Maybe even outside of physics.

[@ButWhySci]

Is it not a cyclical argument? If there wasn't conservation of energy then there wouldn't be the symmetries to create/define. At least that's what I interpret. I could be wrong.

[@algolin]

@@ButWhySci You are right in the sense, that for every conserved current there is a symmetry of a Lagrangian (so Noether's theorem is an equivalency). But symmetries seem to me more fundamental than conservation laws.

[@Azarathos]

​@@algolin Agreed. Another way to think about conservation of momentum is that it's a consequence of Newton's 3rd law. Granted, you can also argue that it's the other way around, i.e. that Newton's 3rd law is a consequence of conservation of momentum, but Newton's 3rd law (the law of equal & opposite reactions) seems more fundamental* to me than conservation of momentum. *Sidenote: As a fun analogy to explain why I find Newton's 3rd law to be more fundamental than conservation of momentum, consider the game of chess. Bishops start the game either on a black square or on a white square, and they can only move diagonally. Since diagonally-touching squares on a chess board are always the same color, then a consequence of the bishop's "diagonal-movement law" is that they are bound to spend the whole game on squares that are the same color as the square they started on (e.g., a bishop that starts the game on a black square can only be on black squares throughout the game); this would be the resulting "bishop color conservation law", which I think we can all agree is less fundamental than the bishop's "diagonal-movement law".

[@KuldeepChauhan333]

This is profound. The way you have explained 4 variables (Including Ct) with a 3 axis graph is amazing . I have been watching Space Time explanations for a while now and I find this really intriguing. Thank You Sir !

[@victorgrazziani]

My guy, I absolutely LOVE your channel. Your didatics are above what one would expect from a free youtube video and I wish I could donate to show my deep admiration for your work. I'm a insatiable curious person and you help me keep the learning ball rolling so effortlesly by teaching with those funny animations, you've helped me understand so many complex topics that I had seen before but didn't fully grasped the concept until I saw the way you break down each pice of information. It helps me contextualize and fit everything togheter in my mind's puzzle about how the universe do it's thing and feeds the flames of my imagination. I don't usually comment on videos but you deserve it, thank you so much! Hope the very best for you and everyone out there sharing knowledge for free. (Sorry for grammar mistakes, self english learner)

[@robertvann7349]

M=E/c² is how God created the universe . This is how physical matter that never existed was created by energy, same way nuclear reactors create non existent energy. Intelligent design argument? Logic science 101 Law of contradiction A=B impossible contradiction subjective illogical reasoning Law of non-contradiction A isn't=to B objective absolutely true logic A nothing caused evolved the contradiction effect of = B something This is A=B impossible contradiction, nothing can never cause something, it can never be demonstrated nothing caused the effect of something, simple In labs A isn't=to B is observed A nothing caused the effect of = A nothing B something caused the effect of = B something Now, A non intelligence caused evolved into the contradiction effect of = B intelligence This is A=B impossible contradiction subjective illogical reasoning Your intelligence came from an intelligent source logically which is absolute truth A isn't=to B objective absolutely true reason. EVOLUTION is A=B impossible contradiction A no brain organisms caused evolved into the HEINOUS CONTRADICTION EFFECT OF = B a brainiac organism This is A=B impossible contradiction subjective illogical reasoning. A prokaryotes no nucleus, mitochondria organelles, and never mitosis and meiosis in dna caused evolved into the HEINOUS CONTRADICTION EFFECT OF = B eukaryotes with dna magically making a nucleus, mitochondria organelles and mitosis and meiosis from nothing in prokaryote dna instruction. A=B impossible contradiction subjective illogical reasoning Cool eh...😎👍❤ Have to love simple logic science 101.

[@helloelianamilena]

I just got to say... Your English is amazing!

[@shuncho7844]

@@helloelianamilenaagreed

[@anywallsocket]

FINALLY. Countless times I've seen people explain it as if they've done so completely, either by dimensional analysis (simply calling c^2 a "conversion factor"), or some other hand-wavy way. At some point everyone just seems to say "that's sufficient for me!", but I have been unable to alleviate the itch that the first c is our motion through spacetime, and the second c is the real conversion of matter into energy -- for what is mass but locked up energy, and what is this energy in its purest form if not light?! Thank you

[@SolidSiren]

But he also explained that c^2 is a conversion factor. He just explains how/why.

[@nanamacapagal8342]

The dimensional analysis method shows that it could work but it doesnt explain what makes it so different from the formula for kinetic energy (which is also in units of mass * velocity ^ 2). This does actually explain a LOT of things

[@anywallsocket]

@@SolidSiren c^2 is simply a ‘conversion factor’ if you’re satisfied with that like a lot of explanations here on utube, but it’s also much more than that if you are smart and inquisitive. Dimensional analysis only truly makes sense when you understand what’s going on within those dimensions.

[@HenryLoenwind]

@@SolidSiren It stops being a simple conversion factor when you realise c² is 9e16 m²/s². The number is a conversion factor, but the units...

[@SolidSiren]

@@HenryLoenwind it's necessary

[@rogumann838]

You just blew my mind, I have always known and accepted from relativity that time seems to tick slower the faster you go (time and speed relative to something else), but I have never once heard that its because we move through spacetime at C. In general I would have to agree that this video is a bit more harder to follow compared to your other videos, but those other videos are amazing!

[@vhawk1951kl]

Now compare the passage of time first when waiting for a bus and waiting to be executed by firing squad. Now suppose that the bus driver will be executed by firing squad the moment you board his bus.

[@coobit]

You have given me a gift of understanding some of the logic behind the spacetime construction. Thanks.

[@felixpeltier6164]

wow! this is the first time ive been able to understand the concept of relativistic mass. I've always heard the dumbed down explanation of "at high speeds, objects gain mass" and i thought that the energy of the object was being directly transformed into massive particles. Thanks for this video, guys. def my favorite one yet!

[@angeldude101]

There's no such thing as "relativistic mass." Increasing velocity doesn't increase mass to compensate for the increase in energy; it instead increases momentum through space to counter the increase in momentum through time (aka energy) so that mass stays constant. Acceleration is little more than a rotation between time and space. The reason there's confusion is because E = mc² is either incomplete or just _wrong._ It's missing an extra spatial momentum term on the left hand side, or E should be E₀ to explicitly indicate that there is no spatial momentum.

[@robertspeedwagon982]

I love how the visuals in this video are so weird for no reason it's amazing

[@todddaniels1812]

"No one knows why momentum is conserved" ... Emmy Noether enters the chat.

[@qwfp]

I feel like this video was harder to follow, compared to your previous videos. Why do we move at constant speed through space time? Why does adding time dimension suddenly makes velocities not relative?

[@accountthatillusetocomment3041]

1- This is a principle of reality. It doesn't explain why, it just says it is, kind of like why light has no mass or why do particles have charge. 2- Basically, the theory says that to make the speed of light not relative to observers traveling at different speeds we need to modify time, since speed = d/t, we can modify "t" so that d/t invariably gives a constant value for the speed of light.

[@equaliity2719]

Our velocity through time and space being constant makes so that everything moving relative to us have a vector of c, so if they are moving in space(relative to you) they are slower in time, maintaning a constant speed in time and space

[@watzyh]

basically everything move at same constant speed C, nothing relative. but a lot of objects in universe 'looks' move at lower speed, time dimension is where the missing velocity goes. if you 'stationary' all your velocity goes in time.

[@fernandoportal5422]

​@@watzyh this is a nice way of seeing it.

[@NeroDefogger]

hahahaha I love it, people actually notice that nothing makes sense to them, they literally see word salal, because it literally IS word salad

[@Sir_Uncle_Ned]

A lot was slotted into place with this one! I now know the mechanics behind time dilation! As movement through space approaches c, the movement through time slows down to compensate! Well, that’s my mind blown. Welcome to the “Ned’s mind blowers” playlist!

[@sonpopco-op9682]

Except that is wrong. Time is the product of observation, ie: a local effect. Different location while all existing now are only the 'present' of the observer. All else is the past, a measurable disparity. Motion changes relative distance and time. The apparent dilation is only relative to an external observer. The object moving does not experience weird effects, it still takes a year to go a year.

[@marcon33]

Like muons in upper atmosphere being measure at the surface of the earth after they disappeared in some tiny amount of tine

[@sonpopco-op9682]

@@marcon33 The incoming muon can be better explained thus. Moving at .997 C means that every nano-second ( 10^-9) it moves about 1 foot. With this movement it becomes closer by just less than that same nano-second, and relative to the observer it becomes younger by that amount. Relative to the observer the muons loses 'age' as it approaches. This has the effect of it appearing to move faster than light (the D remains the same, while the relative T is smaller). The muon does not de-age, nor does it change its speed OR the distance travelled. The effect occurrs only at and WITH the observer, and exists because relative to that observer it is moving at nearly the "speed" of time; 0.997 C ( which we should call the speed of causality)

[@HenryLoenwind]

@@sonpopco-op9682 The moving object still observes the time portion of its movement vector as being at right angles to its space axis and being of length 1c. The resultant rotation of its coordinate system matches the "flattening" of space that's part of those dilation effects. And no, it's not just an observation effect. When you bring an object (e.g. a clock) up to speed and then back to its starting point, it will have experienced less time than an object that stayed there. While those two objects could debate which one is moving and which one is stationary while moving at a constant speed, only one of them will have experienced acceleration and deceleration.

[@sonpopco-op9682]

@@HenryLoenwind at right angles? More math mumbo-jumbo. You are introducing an imaginary dimension and giving it magical properties. Not allowed. time is pure perception. Anything you measure on the object you have applied forces to will still be your observation.

[@aidenpeltier786]

If you made a discord server and invited a group of people to watch the video prior to release and give some insight as to what might be understood coming into the video by most and what should be elaborated on, that might help give people not as familiar with physics an easier to follow video to watch; with that being said, this video was still great and informative and pretty easy to follow. The graphics definitely helped as well. Keep up the good work!

[@OslerWannabe]

BRILLIANT! In the 55 years since i first studied all this, I've never heard this particular facet explained so clearly. Subscribed, and I'll be back..

[@Mr.Carbon1]

One thing you forgot is that it is actually E with a subscript 0, meaning that it is the energy at rest not just any energy

[@tenv]

Acollierastro?

[@declandougan7243]

Yeah, but he explains that mass only has meaning in the proper frame, so being at rest is implicit.

[@Mr.Carbon1]

@@tenv yes

[@euanthomas3423]

She's still right.

[@nice3294]

This is such an interesting way of putting E=mc², amazing vid!

[@gimmedaloot754]

This has been a thorn in my side for 20 years.. never had the time to investigate it through all my physics courses at the university. Dynamics, statics, thermal etc…no explanation was ever attempted. It was just a fact, a baseline to move from. Thank you. That itch has finally been scratched and I can die in peace…🤣😇😎

[@Christian-os3kk]

I love the little touch of the digitized Mozart's Requiem at the start. It nicely represents the true DREAD emerging from the philosophical implications of the equation in question.

[@TheFinagle]

On a side note this is also where time dilation from motion comes from. (you brush on that with the fission reaction example) Your 4D speed is locked at c - always, so if your moving rapidly through spacial axis of the 4D spacetime there is "less room'" in that c value for movement through the temporal axis. (Technically ANY slight motion would come with the tiniest amount of time dilation, its just negligible until you reach reasonable fractions of the speed of light)

[@TheVenerableMrKrieg]

Hearing your words over 1:45, it finally clicked why I never got it until now. E = M to the assless power times C squared. My attention span has always just given out once it realised the mass was assless and realising that was all it took to power through!

[@pangeaproxima3681]

_...assless?_ you mean with _no ass?_

[@muumia4]

Keep up the good work! Loved the twilight reference at 0:34

[@BlackbodyEconomics]

By far, one of the best explanations of E=MC^2 I have ever heard. Well done!

[@semajgraham5849]

wait, does this also explain why they say "the faster something moves, the slower time is for it"? This is all really fascinating stuff!

[@kylelochlann5053]

No, all identical clocks tick away at the same rate, everywhere, and under all circumstances of the motion and orientation. This is fundamental to relativity (Local Position Invariance and Local Lorentz Invariance, respectively).

[@pon1]

Yes, the faster you move through space, the slower you move through time. Though you always experience a second being a second since everything else moving at the same speed slows to the same rate of time as well. The effects of timedilation is seen relativistic to other's frames of reference. This also means that there is no speed limit of c in your own frame, c represents infinite speed for you, but since time slows down you would effectively never move faster than c in other's perspective, as their time appears to move faster in your perspective. To them you are approaching c but never quite getting there while they are growing older seeing you attempt to reach it. For you, you surpass c while seeing them grow older at a faster and faster pace. Of course you can never reach infinite speed in your perspective (as it is infinite), just as you can never reach c in their perspective.

[@kylelochlann5053]

@@pon1 That is completely and perfectly anti-relativistic. Correctly, the faster a traveler moves through the observer's coordinates the slower they move through the observer world-time. The "c" in relativity is the norm of the vector tangent to a world-line [g(U,U)=c^2], which is why inertial observers measure the local vacuum speed of light to be "c" (light is restricted to the null structure of the gravitational field). It is fundamental to relativity that all identical clocks tick away at the same rate, everywhere, and under all circumstances of motion and orientation (Local Position Invariance, Local Lorentz Invariance, respective].

[@pon1]

@@kylelochlann5053 I just said that. What did I say that goes against what you said? I just said it in language the people can understand instead of your jibberish.

[@kylelochlann5053]

@@pon1 The "gibberish" is called "relativity" which you patently disbelieve or don't understand.

[@burnttoast9768]

Beautiful, the nature of the video is very complex but you simplified is as much as you can.

[@sherrinisadumbass211]

I don't think I've ever shouted with joy at an educational video before, this made so much sense in such a well articulated way. Thank you ever so much for this genuinely eye opening video!

[@djenning90]

This is really well presented and explained, thank you!

[@marhensa]

yes I had this question for very long time. everyone seems talking E=MC² without even know what C does in that equation. so when ChatGPT came around, this is one of the first questions I asked to it. but it still can't satisfy my curiousity. WHY IS IT HAVE TO BE A SPEED OF LIGHT, AND WHY IS IT HAVE TO BE SQUARED? it's must not be just because it's a mumbo jumbo big numbers. this video in the other hand, satisfy my curiousity. thank you!

[@eschdaddy]

I always thought it was based on kinetic energy = 1/2 MV^2. So, I wondered what happened to the 1/2. Great explanation!

[@aaronhoney2217]

Yes, the relativistic kinetic energy is related to E=mc^2 by relativistic KE = mc^2 -m0c^2 but not the non-relativistic KE = 1/2mv^2. The non-relativitic KE=1/2 m x v^2 applies when ‘v/c’->0 only for VERY SMALL ‘v’ compared to the speed of light v

[@eschdaddy]

@@aaronhoney2217: Wow, need to go over it to understand it better, but thanks! You definitely made my day!

[@FoxofWallstreet]

@@aaronhoney2217 relativistic mass doesn‘t exist btw. Today we just take the Lorentz factor separately into the equation

[@MrOvipare]

We know why momentum is conserved, this is because our universe has translational symmetry. From observation, we see that the laws of nature remain unchanged if you move 1 meter away from where you are. From this observation alone arises logically, through Noether's theorem that there is an inviriant quantity associated with this symmetry and we call it momentum. It means that as long as translational symmetry is a good description of the actual world, momentum will be conserved. There are two other important symmetries that have their own invariant : Rotational symmetry -> conservation of angular momentum Time symmetry -> conservation of energy

[@sacsingh108]

So far the best intuitive explanation I have encountered.

[@markpmar0356]

This is a useful primer, I'll have to admit. It doesn't quite explain how C or C squared is a conversion factor but it moves me in that direction. No pun.

[@psykoj]

My takeaway: everything movies at the same speed through spacetime (c). So even though I’m walking and a car appears faster than me, we’re going through the same speed in spacetime - I.e the car moves slower in time than me. I.e the car experiences less time. A photon would experience no time because it’s movement is essentially only in space. Phew! Lovely way of thinking of it. Though I did get a little lost with the momentum stuff. Doesn’t the whole equation have a momentum component? How does that fit in? E2=(mc2)2 + (pc)2

[@FoxofWallstreet]

Wait, I know the answer for that. The full equation kann also be written as: E=y*m*c^2 (y being the Lorentz factor) and the full equation of p=y*m*c

[@williamtait3700]

In reply 1 the Lorentz factor tells how much the cars time has slowed. It also tells us how the car has shortened. I find it easier to realize that the car is made up of charges separated by EM fields. The fields can only go at the speed of light and no faster. If the charges in the car have a net velocity this must come out of the velocity which give the car atoms their length. Of course the changes are so very small.

[@williamtait3700]

Regarding the photon having "no time experience". It means that the photon is equivalent to an entity where no other spatial motion is possible because all its motion is taken up in the unidirectional forward c velocity. However, we know photons oscillate between field extremes over time. Therefore the field oscillation is not an actual distance oscillation but rather a physical field property oscillation which is not any part of movement as we know it. It is a perfect oscillation in some field or space fabric. Note photons can keep oscillating over billions of years.

[@krumplethemal8831]

Velocity and rate of time are exchanged on a spectrum. The greater the velocity, the slower time passes. P1. If you could zero out your velocity to never move your x,y,z coordinate relative to space itself. Time would speed up!

[@malecsobie1777]

the best visualisation of 4 dimensional world I've ever seen. Great video btw. Everything well explained

[@Ikbeneengeit]

We kinda DO know why momentum is conserved, it can be derived from the fact that the universe has translational symmetry. Emily Noether proved it.

[@jayde4872]

Well, why does the universe have translational symmetry?

[@user-xh9pu2wj6b]

@@jayde4872 that's a more philosophical question, really. Basically, it all comes from the assumption that we aren't in any way special. Our place in the universe as a whole is no different than any other place, if we discard every bit of matter and everything and just sit in completely empty space. And, fun fact, that's definitely not the case in general relativity where energy and momentum can only conserve locally because space-time itself is clearly not uniform.

[@tuseroni6085]

this is strange to not include the full equation: E^2=(MC^2)^2+PC^2 which covers the energy of a massive particle plus its momentum but in massless particles simplifies to E=PC and in massive particles not moving through space simplifies to E=MC^2

[@BalrogsHaveWings]

Thanks for this! Now all I need is to wiggle this into a conversation at the pub amd explain it before I forget what I was talking about.

[@Govstuff137]

Am I correct too say? If one could sit motionless at the singularity at the point where big bang started then time is moving away from me at the speed of light?

[@dominikfrohlich6253]

This also elegantly explains why you are moving slower through time as you are moving through space. When you move at the speed of light, time stops (for you). The combined speed of your movement through space and time is always C

[@IceMetalPunk]

It's elegant, but it kind of raises the question: if things seem to move slower in time as we move faster precisely because we observe everything to move at "c" through spacetime, and thus faster in space = slower in time to compensate... then how does the speed of light remain constant in all frames of reference? I know it comes out of Maxwell's equations, but from this physical framework of "constant spacetime speed", how does it fit?

[@Bodyknock]

@@IceMetalPunk Actually nobody knows what the speed of light is invariant in all reference frames. That's literally an assumption Einstein makes based on experimental evidence related, like you said, to Maxwell's equations, but that assumption isn't something that's mathematically proven directly from them. It's really basically just an "educated guess" that it's true. But once you make that assumption, all of Relativity is derived directly from that. And experimentally Relativity has held up extremely well as a mathematical model of the universe, so that lends a lot of experimental evidence to the speed of light being the same for all observers (because if it wasn't then Relativity wouldn't work.) So the short answer is nobody actually knows why the speed of light is invariant, it's truly a mystery because it's pretty unintuitive to our everyday experience in the universe. But "numbers don't lie" and experimentally it really seems to be the case because, when you assume it's true, Relativity is the model that results and it's a fantastic predictor of real world physics.

[@williamtait3700]

The propagation of photons and also the continuous instantaneous EM fields produced by charges must depend upon charge location (mass location) for direction and intensity only. The speed of travel must be a constant function of the media (space) between all charges. This is good evidence that space is some kind of physical reality rather than nothing.

[@svetlicam]

We could see it also in a different way. As you say momentum is mass times velocity. Mass is then momentum divided by velocity. Which means that mass is point in space that has certain potential energy, this energy is then translated to kinetic by plain fram of reference of final possible speed distribution, and this plain of distribution is simply c squared. So any point in space that possess some potential energy can be converted into kinetic energy which is distributed through finial speed, speed of light plain. It doesn't matter which direction. Because it is in all directions. Also can be converted into kinetic energy with speed of light and then becomes photon. I hope you get the point of my perspective. This is why this equation connects classical physics to quantum mechanics, because is valid in both frame of reference.

[@charliecharliewhiskey9403]

Next time someone tells me I'm lazy for sitting still I'll say "Actually, I'm moving through time at the speed of light, I'm being very energetic"

[@Radiers]

I don't know if I am onto something or not but hear me out here: Inertial or gravitational mass doesn't make sense in this 4D spacetime(where everything travels at a constant velocity,c). Mass can be defined as the property of an object that resists acceleration(a = F/m). However you CANNOT accelerate OR decelerate in this 4D spacetime as everything HAS to move at the speed of light in spacetime. Your velocity through spacetime(combined) is a constant,c. Since Space and time are on two different axes,you can represent your velocity as a combination of your velocity through time and your velocity through space. Think of normal everyday acceleration(the one that u feel in your car going from 0 to 60) as the part of your velocity through time DECREASING and your velocity through space INCREASING. This is the reason why time dilates at significant fractions of the speed of light,since velocity through time has to compensate for the increase in velocity through space. This compensation is required to keep the object moving to spacetime(combined) at only one velocity,c.(Remember that all objects have to move through spacetime at velocity,C)

[@oberonpanopticon]

1:15 I was under the impression that binding energy had mass, I could’ve sworn I heard somewhere that something like 98% of the mass of nucleons came from the quark’s binding energy and only a small percentage of the mass came from the higgs… field? mechanism? boson? I really don’t know enough about physics

[@vinevicious]

that is right

[@averagecornenjoyer6348]

that's true but there's some nuance here for the sake of mental sanity about what's massless and what's mass..ful? really, here we're considering binding energy to be "massless" just for the sake of saying it's energy

[@DrDeuteron]

Binding energy is negative, so it subtracts from mass. The positive mass from quark binding is a whole nother thing.

[@ButWhySci]

This is a good question. Binding energy is a general term en.wikipedia.org/wiki/Binding_energy . It can refer to multiple forces. The binding energy you are referring to is that of the strong force inside a quark. You are correct in that, since it is confined, it has mass and it doesn't really change. Then there is the binding energy due to the strong nuclear force (different force than the strong force). When two nucleons approach, their produced pions can interact with the other nucleon, and to spare you the details, this interaction permits them to lower their energy state. Since they now have less energy they have less mass. So when you fuse two nucleons, you lose some mass to "binding energy". The same thing happens in regular chemistry when electrons bind with other atoms (In exothermic reactions). This is also called binding energy. And just like with fusion the new molecule has less mass. Though, the difference is miniscule compared to fusion. If you are more curious I highly recommend my last video on fusion where I discuss binding energy in depth.

[@oberonpanopticon]

@@ButWhySci Thank you for the explanation! I think I will check out your other videos and see if they’ll help me understand this stuff better. I’ve often found that the terminology in particle physics can get pretty confusing.

[@tom-kz9pb]

I had noticed before that e=mc2 was similar to the kinetic energy equation. Thanks for confirming the connection. From college physics, I recall how e=mc2 falls out as corollary of the more general Lorentz transformation, but for some reason it took decades before it dawned on me that this was the "Lorentz" transformation, not the "Einstein" transformation. Because of Einstein's fame and probably because of the iconic, frizzy hair, we tend to forget how the foundations of special relativity date back earlier, to the 1800s. Einstein may have also taken some ideas without full attribution from the contemporary mathematician, Hilbert. But we will be fond of Einstein's genius, anyway, especially because of the frizzy hair.

[@nuance9000]

Einstein's deification is our own making. He stood atop Maxwell's shoulders-

[@michaelgarrow3239]

Um,,, frizzy hair is why you are an Einstein fan boy? 🐷🎶🎵

[@attica7980]

Google for incorrigible plagiarist.

[@flagmichael]

They really are the same, when we accept the kinetic energy has to be a characteristic of the object.

[@peymanrostami7753]

I had the same question as you in high school. I could find the answer at university (although I was studying engineering). take a look at the answer I provided above.

[@rianmacdonald9454]

Really enjoyed this video - great work guys.

[@banpridev]

Lol will need to rewatch this, I did not know about the relation between space-time and this equation, like I know all the other concepts, but this was the missing link and it just makes sense. Thank you for this.

[@feynstein1004]

You don't know why momentum is conserved? Emmy Nöther would like a word with you

[@k1m6a11]

Yeah maybe I'm dumb but this video could have been a lot clearer.

[@davidmurphy563]

Hmm... Well, what he said was absolutely spot on - this was 100% absolutely accurate science and from an interesting perspective to boot - but I'll grant there was a lot of prior knowledge assumed... For example, he referred to the "dot product" at one point (without actually saying the term) and without explaining what the term "vector" or a scalar quality is. Much less explaining what the operation is or why it was relevant; he just said it's multiplying (which is true). You don't need to be a genius to learn this, but it needs study for sure. Nobody will guess it from this. 0% dumb for not. Yeah, I think on balance your comment is fair, he assumed a knowledge of maths which most people have never been remotely taught. If you do know it then you're nodding along but gaining the necessary grounding is many videos of information. Yes, the groundwork was lacking. You're certainly not dumb for not following. The problem is that with any layperson's explanation you kinda have handwave things or you're just offering an academic course. It's hard balance to strike in a short video format with grand aspirations.

[@lifeunderthemic]

This is normal sleight of hand. He couldn't provide it if he tried as he is a makeup of irrationally contrived abstract concepts through parroting as a youth that was provided propaganda.

[@k1m6a11]

@@davidmurphy563 I pretty much agree with everything you said. Thanks for the measure of validation.

[@davidmurphy563]

@@lifeunderthemic Nothing of what was said was irrational or sleight of hand. It was accurate science which is based on a mountain of evidence. The satnav on your phone uses relativity calculations to work; this has practical everyday use. The criticism is that this video boiled many 1 hour videos into 8 mins. Not that anything said wasn't entirely accurate; it was.

[@Harpoika]

It feels eerie when you understand this and start thinking about all the ways we divide energy into many other forms and its essentially always about just adding package that slows it down. And in our universe how much slower is always referred by time and distance e.g. spacetime. 🤯

[@Kaemmer23]

6:59 does this have anything to do with scalar light? I’ve heard of it existing but don’t know much about it. Apparently has the potential to create instantaneous communication devices or directed energy weapons if used the wrong way

[@stefan_popp]

I would suggest changing the 'm' and 'c' to be lower-case, otherwise you'd say Energy is equal to molar mass (M) · Coulomb (C)².

[@davidmurphy563]

"The first is that momentum is conserved. I don't know why, no one knows why, just in the universe momentum is conserved." I never really got the whole mystery over momentum being conserved. If you accept Galileo's Principle of Relativity then all reference frames are equivalent; there's no absolute reference frame. No Aether that we're all passing through. This is about as settled as science gets. So, Newton's 1st follows from that. Do nothing, nothing changes. If there's no force, then being at rest and constant motion are the same state. So of course momentum is conserved, how could it not be? If, like me, you've ever modelled the solar system or anything in 3d for that matter then conserving momentum is what happens when you don't programme anything about momentum. You just let it run, things collide. Stop at any stage and tot up your momentum, and it's always the same. How could it not be? That's the default. Conserved means it doesn't change and it doesn't change because nothing is happening to change the total, just how it's divvied up between things.

[@davidmurphy563]

Btw, your vector arrows above p and v are the cutest I've ever seen. They're damn adorable! Lovely video as always, great way to communicate the science. :)

[@nicholasauwaerts2280]

momentum in SPACE is not absolute but it is in SPACE-TIME. Space time is the absolut reference frame

[@davidmurphy563]

@@nicholasauwaerts2280 Spacetime is a field, not a frame. There is no absolute reference frame. If two spaceships pass in a void then it's equally valid that one frame could hold spaceship A stationary and B moving and another could hold the B stationary and A moving and they're equally valid because no experiment could ever favour either of the two statements. It's very counterintuitive and overturned two millennia of thinking; Galileo isn't considered one of the greatest thinkers of all time for nothing.

[@noahway13]

@@davidmurphy563 In a way, couldn't a Field be called an aether? I can't seem to find a definition of Field that satisfies my mind. There is no 'empty' space, correct? How do they detect gravitational 'waves'? They say there is a ripple ( A wave attribute. Just a small wave, now that I think about it) in the FABRIC of space-time. What is the difference between a 'fabric' and a 'field' and an 'aether'?

[@davidmurphy563]

@@noahway13 Well, we're all free to define any word to mean anything we please but usually "aether" is taken to mean an absolute reference frame (coordinate system) that we all exist in. This was famously shown in the Michelson-Morley experiment to be untrue; much to the astonishment of scientists at the time. A good part of Einstein's genius was accepting the experimental evidence. It had been noticed that light behaved like a wave, so as all other waves propagate through a medium it was assumed there was an underlying medium to the universe that it travelled through. They did the experiment and it doesn't exist. If you're travelling at relativistic speeds on a spaceship but not accelerating, then you are at rest. It's perfectly valid to say you're sat still and the galaxies around you are moving, not you. Weird way to look at it but you can. That doesn't mean there isn't a "fabric" of space with gravitational waves and all the rest (the field). Just that your perspective of it - drawing a coordinate system with you at the centre - is perfectly valid. As is every other. I'm not saying there's no coordinate system, only that there isn't a preferred one. Relativity is the explanation of how all these frames coexist simultaneously. It's the maths that makes them all gel together.

[@Mydumbselfsays]

THIS IS THE EXACT VIDEO I NEEDED! I'VE BEEN SEARCHING FOR AN ANSWER FOR YEARS NOW! THANK YOU THANK YOU THANK YOU

[@TacticusPrime]

So our moving through spacetime at c, when at rest, is what determines the energy of the directionless momentum phanta that we interact with. So it isn't just the momentum of the thing being converted to energy that determines its energy relative to us. It's our momentum too. That makes sense now that I've written it out.

[@KUWAITGRIPSVEVO]

1:42 e=m assless c^2. Leg day skippers in quantum shambles

[@vjreimedia]

I didn't understand a thing.

[@tanish1563]

Don't worry there are a lot of them

[@eyeofthasky]

7:30 the revelation i got from that was that motionless things experience time as 100% (=c) but the more motion u have (since c is a constant) the smaller the portion of this velocity in direction of the t-axis, hence things in motion experience time to a lesser degree. like a clock in space would tick faster than on earth. my (anthropomorphic) explanation was always, gravity pulls not only mass but it also pulls on time forcing it to slow down, but since gravity=acceleration and thats in turn velocity, both metaphers are the same, just seeing the coin from the other side.

[@lincolnkaden7758]

Cool… That actually made perfect sense! Well explained. Thank you!

[@kelevra5240]

i think i see why time dilates or length contracts sorta at light speeds now. but err yea this one aint as easy as some of your other ones

[@Squid2214]

Everything needs to move through spacetime at the speed of light. If you're motionless in SPACE, then you're moving through TIME at the speed of light. If you're moving at the speed of light through SPACE (like a photon), then you cannot be moving through TIME. Thus, moving somewhere between the two speeds would mean that you're moving through time slower than if you were motionless (time dilation)

[@angeldude101]

@@Squid2214 Moving at the speed of like like a photon is more like moving at an equal rate through space and time. Actually moving entirely through space with 0 momentum through time would likely be a tachyon and would require imaginary mass.

[@Squid2214]

@@angeldude101 Photons do indeed experience zero time. Since neutrinos can change state, that means they have to experience time. That's how we were able to predict that they don't quite travel at the speed of light like originally thought. Photons do not change state. Another way to think about it is length contraction. The faster you go in space, the shorter your travel distance seems to be. If you go the speed of light, your travel distance shrinks to 0 exponentially (which means it takes you no time at all to cross the entire universe, at least in your frame of reference)

[@smileyr6s838]

Physics just great. It's so impressive to fully grasp all the systematic connections between literally anything. As my professor once said: Physics is not math, it's the language of the universe. And I truly believe that we are just getting started to explain our universe and with that EVERYTHING: Side note: I am writing a physics exam in about 11 hours so please accept my excitement and enormous respect LOL

[@jesusbermudez6775]

Yes, thanks for the video. However, as I am completely new to all of these concepts I will need to see it again a few times to grasp many of the concepts described here.

[@-mwolf]

that 4d/spacetime visualization really helped!

[@newton-342]

Here's my take on the topic of this beautifully animated and beautifully spoken video. I disagree. E = mc² (according to Einstein’s theory) always holds. You don't need to convert energy. I thought that for a long time. I think that the truth about this equation is, if the energy of an object increases so does its mass. If the mass decreases, so does the energy. The calculation for that is pretty straight forward. Off the top of my head, I can come up with one scenario, where actually all of a particle’s mass is “converted” into energy is, when a particle meets it antiparticle, e. g. an electron and a positron collide. A photon is created with the energy of 2*m_e *c², which is in the gamma (or X-Ray) spectrum. After that conversion E=mc² can no longer say something about the particles, because they don’t exist anymore. However, this formula tells us: you can put that photon’s energy into _something_ and that _something_ will gain the mass m=E/c². I imagine you could create two antiparticles again, out of thin air (I mean vacuum). Now onto the second thing that drives me crazy: c_0 = 299,792,458 m/s, per definition of the meter. You can’t move through space and time at something meters per second. Distances in spacetime shouldn’t be measured in meters, rather a mix of meter and seconds. But I read in Wikipedia, that spacetime is not a four-dimensional Euclidian space, like I always thought it was (thank you @ButWhySci that I know that now!). The mathematical construct is to multiply a time delta by c_0, square it and subtract the square of a space distance, to get s², whatever that means in the real world. Also, I don’t think Einstein’s professor Minkowski proved that we live in a four-dimensional reality. For as much as I know, general relativity disagrees with quantum physics and neither of them can prove the other wrong. But we know: one of them or both of them are wrong. From a theoretical standpoint: no physics theory can ever be proven, only disproven. 3:38: suddenly, _everything_ is relative: What it means for velocity through Minkowski spacetime to be constant is: you slow down if you move faster though space (that is you move slower in time) and you speed up if you decrease your velocity through space. Also note, you yourself will percept that change in time-velocity not own yourself, but on others who have a different velocity (though all have the same speed, that is magnitude of velocity). And these others will see your slow down, just like we can see experimentally that Muons only survive the journey from sun to earth, because their time is slower than ours’ (from our perspective). 4:04: But why, should the conservation of momentum also hold for velocity through spacetime? 6:58: But why??? You lost me there, actually. After that, it seems to me, that there is much hand waving. What do I take away from this video? First, that I don’t know a lot about relativity. Secondly, that the mathematics of relativity is really not suited for giving a fundamental understanding of E=mc². But I also take away a few more minutes thinking about relativity and learning about it, so THANK YOU! PS: sorry for the puns

[@user-ti6ix5tn2o]

Yes I agree that using poison dagger with 90 points of critical damage is good but it is outshined by bloodlust one handed axe. Reasons why, first the axe does 20% reduction per .65 second of enemy's current HP. Second, it provides a trail to affected enemies and following the line of trail gives the player 75% speed boost. Third, continues strike grants 15 HP Regen and if you have an item that double or increases your attack speed you would easily recover more faster. And lastly the item is deadly when paired with other items that synergies with it well. Having cape of kings, amulet of Ra, mercury's boots and genie's ring; you'd be OP.

[@robloxfanboy86]

Wake up babe new but why video just dropped

[@heretichazel]

this finally made it click for me! it feels so simple now that I have the proper framework to think about it, I've always been interested in relativity and stuff but didn't understand the "why" behind time dilation

[@Rudxain]

For anyone confused, I remember a video where they explained speed as an arrow with constant length (c) and variable angle (space-time trade-off). There's a horizontal space-speed arrow, and a vertical time-speed arrow. The length of both straight arrows depends on where the angled arrow points. Thereby explaining why nothing can go faster than c (in time or space), and showing how there's no such thing as "absolute speed", as all speeds are just fractions of the speed of causality (c)

[@Ajay-kz9ns]

Great video. I still don't understand any of it

[@DanielBro42]

lol same

[@danielhodges514]

is this why photons do not experience time, because all of their motion is only in space?

[@declandougan7243]

Yes. You could also phrase it as, “the energy of photons is exclusively space-like.”

[@tylerdavis3]

I’m still confused on how momentum squared is equal to the speed of light time mass squared. Are we neglecting a relative observation of velocity and only using C, I think so, but why? Edit: so I guess my question really is that this only works when in a proper frame? Or can you take into account velocity moving through space too? I suppose I’m still looking at things through Newtonian goggles and having trouble seeing a relativistic overview.

[@cobar5342]

Mind-bending stuff I shall need a lot of spacetime to digest it. Great video

[@suicideistheanswer369]

I am going to watch this a few times to fully understand. I don't understand what it means to be moving through time at c speed.

[@BerryMcCockiner]

That's just the base rate at which everything moves through time(the 4th Dimension). This would account for something that looks like it isn't moving. It would still have energy. im dumb but i hope this simple bit of knowledge can help you visualize light and its relation to time.

[@MagruderSpoots]

No one else does either because we don't know what time is.

[@mikeoxmall69420]

The universe is being flung along a 4th dimension like a shotgun blast at C. That 4th dimension is time.

[@matterasmachine]

Those postulates are just wrong. I gave better with the same predictions.

[@Benson_aka_devils_advocate_88]

It was originally written as M=E/C2 and I forget the difference in nuance but I remember someone explaining that there is a slight difference none the less

[@Bialy_1]

There is literally zero difference...

[@runenorderhaug7646]

To be honest for me and why I think it sounds odd for some is more the question of what is a equivalence supposed to represent when we think about them in physics formula. We of course shouldnt get too locked into this as formulas rareily represent directly the transition themselves, but the prescence of specfically the speed of light can make it odd to explain what is this equivalence representing beyond simply understanding what aspects are operating at a speed of light. You did a good job at showing how to get around that though and the importance of different levels of itnerections within formula like this which is something I think gets skipped over a bit sadly at times.

[@gigamathteacher]

you've triggered hundreds of physicists and physcs students by making the m and c capital in the formula

[@Looking-for-More]

This channel really deserves to be bigger

[@yaroslavbilous8855]

Easily the best video explanation of given topic

[@BeatrisZaharia]

I just love your videos. Nothing more to say

[@MOversteegen]

Its the kinetic energy what comes free after a collision of 2 bodies under an angle (in which you can still use pythagoras) with the speed of light. That's it. Thats why c is used as denotation. Doesn't count for light coz then c^ is still c. Nothing goes faster than that.

[@puschel_hdpuschel3768]

So if I just sit still and dont move, i dont move through space, but i move through time at the velocity c. Thats why a particle that moves at the speed c through space, doesnt experience any time, right ?

[@enriquea.fonolla4495]

even if you sit still, you are still moving. The earth moves, the solar system move and the whole Mily Way moves. Nothing is still in the universe.

[@lumos_blue]

Think you can talk about the possibility of Time Travel next? Specifically to the past?

[@alexandervazquez7016]

Whats the name of the paper shown and refered to at 2:51? I'd love to read his derivation as to why the speed of light is constant using maxwell's equations.

[@Schachmdels]

It is "Zur Elektrodynamik bewegter Körper" written by Einstein. The original paper is in german but there is surely an english translation. But as far as I know you can't derive that c must be constant by Maxwell. One way we work with Maxwell needs that c is constant and we see that the calculations are right while using it but that c is constant comes from experimental data (Michelson-Morley). At least that's what my electrodynamics professor told us.

[@user-xh9pu2wj6b]

@@Schachmdels but can't you kinda derive it by deriving the equation of an electromagnetic wave and noticing that its speed through space only depends on electric and magnetic constants which are assumed to, well, be constant?

[@Schachmdels]

@@user-xh9pu2wj6b Yes, you can easily derive that an electromagnetic wave needs to travel with speed c in a vacuum to solve Maxwell but that’s not quite a proof. The Michelson-Morley experiment wasn’t there to prove that c is constant, it was there to prove that a so called aether exist and with this aether the speed of light should vary (Waves always need a medium, like sound waves need the air. This aether was thought to be this medium for light waves). It was the common expectation at that time that it should vary. But the experiment proved them wrong. Would it be that obvious through the equations the expectation would have been a different one.

[@lucacapperucci8711]

Wait, so is the fact that we are always going C speed throughout space time the reason for why when you go travel really close to the speed of light you go through time slower? I’m thinking of this as a vector with a constant length: the bigger the x component (space), the smaller the y component (time). Is this wrong?

[@brownie3454]

This is mind blowing. Einstein truly a genius no wonder he’s so revered. This is like Beethovens 9th of physics

[@ArchDudeify]

Nice explanation Nice voice too 😉

[@pazitor]

Happy to say I'd known about moving through spacetime at c. Sad to say it had availed me not in grasping the basics, as this video has shown. There are assumptions made about viewer prior knowledge that go whooshing overhead for me, so many a re-viewing are in store once I stop reflexively ducking. Here's hoping I grok it all at some point, as I prefer standing to crouching. Fun, though.

[@walterbrown8694]

We are speaking of energy here - in Newtonian physics, Kinetic energy is expressed as KE = 1/2 MV^2, where V^2 is the velocity squared.

[@KishorKumar-tp3zu]

I Thank the KZbin algo for popping this random channel into my life ❤

[@hypercomms2001]

We are confusing the speed of causality, and the speed of light. One is always fixed, but the speed of light depends upon the permitivity and permeability of the material that it is travelling through.

[@strawwalker8177]

E=mc2 only applies to about 20 isotopes that can have a continuous reaction. Any other splitting of the atom is a negative energy reaction it cost more to split the atom than you receive in energy

[@Sfbaytech]

I’m one of those people who was wondering why it’s squared! Looks like I’ll continue to wonder why 😂

[@wkelly4963]

Great explained. you've got a new sub!!

[@sHuRuLuNi]

You are excellent at NOT EXPLAINING anything.

[@WarpRulez]

My first approach to understanding why it's a square, and cannot be a non-square, is that the units on both sides of the equation must always match, else the equation is just outright incorrect. And if you were to remove the square, then the units would not match, which just outright indicates that it would be incorrect. Of course that then leaves the question of how the equation is deduced (ie. why is it "E=mc^2" and not eg. "E=2mc^2" or "E=1/2mc^2" or the like, in all of which the units would match.)

[@ryanweaver962]

Space moves with time expansion. So amazing.

[@randomstuffwithnofluff7472]

If I had 10 chances to reexplain this to some hostile space alien's to save earth, we'd all be dead.

[@bobespirit2112]

Or you could say, as Newton showed that Force = Mass * Acceleration , and as Force is equivalent to Energy and Acceleration is = to velocity squared, and speed of light is the velocity of Quantum effects, then it follows simply that F=ma is Energy = Mass * C squared. It’s just Newton applied to Quantum effects.

[@mawulidiliza]

Thank you. That was beautifully explained

[@iSmokedEinsteinium]

Was confused about why it was c^2 but not super understandable qoura answers didn't help. This makes sense. The question cataloged in my head has been answered!